Consider the quantum-mechanical wavefunction of a particle of mass \(m\) moving in a linear potential

\[V = \alpha x.\]

The (normalized) wavefunction at \(t=0\) is

\[\psi(x) = \pi^{-1/4} e^{-x^2/2}.\]

Find \(\langle x\rangle\) as a function of time.

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